Line warfare came about as a result of the relative inaccuracy and short range of muskets (famously in Britain, the Brown Bess, which is what the soldiers in your video would have been using). As a result, massed formation firing was essential for maximising enemy casualties (a telling fact was that British troops were commanded to level their weapons rather than aim them). The line was considered as the fundamental battle formation as it allowed for the largest deployment of firepower. Troops in skirmish formation, though able to take cover to avoid enemy fire and use their own initiative, were highly vulnerable to cavalry and could not hold ground against advancing infantry columns.

Since line warfare was necessary, troops were drilled to face volleys from enemy lines so that they could respond accordingly. In your video, if the British troops had broken to find cover from the French volleys, they would have stood little chance of causing much damage to the enemy, or charging them with fixed bayonets if it came to that (as it often did).

Sources:

Dickinson, H.T., "A companion to eighteenth-century Britain," Wiley-Blackwell, 2002. Page 479.

Gilbert, Adrian "The encyclopedia of warfare: from earliest times to the present day," Lyons Press, 2003. Page 76.

In that video, there's a little detail that's historically inaccurate.

The French captain would shout "appretez armes" (make ready) as part of the firing commands. "Appretez armes" was the shortened version of the "make ready" command used in the French army, introduced in the 1790s. In the time of the Seven Years' War, the proper command would have been: "Appretez vos armes"

As a follow up, why are the British soldiers in the front rank advancing with their weapons leveled?

How did they decide who would be in the first rank?